ILL 1978 Problem 22

Let $x$ and $y$ be two integers not equal to $0$ such that $x+y$ is a divisor of $x^2+y^2$ . And let $\frac{x^2+y^2}{x+y}$ be a divisor of $1978$ . Prove that $x = y$ .

German IMO Selection Test 1979, problem 2